Abstract

Spatiotemporal chaos collapses to either a rest state or a propagating pulse solution in a ring network of diffusively coupled, excitable Morris-Lecar neurons. Weak excitatory synapses can increase the Lyapunov exponent, expedite the collapse, and promote the collapse to the rest state rather than the pulse state. A single traveling pulse solution may no longer be asymptotic for certain combinations of network topology and (weak) coupling strengths, and initiate spatiotemporal chaos. Multiple pulses can cause chaos initiation due to diffusive and synaptic pulse-pulse interaction. In the presence of chaos initiation, intermittent spatiotemporal chaos exists until typically a collapse to the rest state.

Lead Paragraph: The concept of transient dynamics may often be more relevant for the understanding of real systems than asymptotic states. Transient dynamics in brain activity is reported, e.g., in perception associated with stimuli, in cognitive function, or as transitions of neurological rhythms in seizure-like disease. A variety of mechanisms for abrupt changes in system dynamics exists, including noise in the presence of attractors, parameter changes due to perturbations, deterministic transients in the neighborhood of an attractor, or deterministic transients as sequential switching between metastable states in the neighborhood of saddles. Chaotic saddles might be important in this context since they allow for more complex dynamics in the metastable state. An abrupt change from spatiotemporal chaos to either the rest state, where all neurons are inactive, or to a state of pulse propagation was reported in a network of diffusively coupled Morris-Lecar (ML) neurons, with possibly long-lived transients in the neighborhood of the chaotic saddle. Our study reveals that weak chemical synapses can make the transients more chaotic, expedite the collapse, promote the collapse to the rest state, or restart chaos upon collapse to specific pulse solutions.

Acknowledgments:

This research is based upon work supported by the Arctic Region Supercomputing Center at the University of Alaska Fairbanks.

Article outline:I. INTRODUCTIONII. MODELIII. TRANSIENT SPATIOTEMPORAL CHAOS IN A NETWORK WITH DIFFUSIVE COUPLING AND NO SYNAPSESIV. ADDING SYNAPTIC COUPLINGV. CHAOS INITIATION AFTER COLLAPSEA. Single pulse interacting with synapsesB. Two pulses interacting with one synapseVI. CONCLUSION